The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1  1  X  2  1  1  1  0 X+2  2  1  1  1  1  1  1  2 X+2  2  1  1 X+2  1  1  1  X X+2  1  0  0  0  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  3  1  1  1  1  3 X+2  1  X X+1  3 X+3  X  1 X+2  1  X X+2 X+1  2  X X+3 X+1  0 X+2  1  X  1  1  1  0
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3 X+3  2 X+3  3 X+2  X  1  0  2  1  3 X+3  0  X X+2  1  1 X+2  X  3  1  2  1  0  1 X+3 X+1  3 X+2  0  0
 0  0  0  1  0  3  1  2  3  0 X+1  X  3 X+3  1  1  0 X+2  3  1  2  1 X+2  X  3 X+3 X+1  0 X+1  X  1 X+1  3  2  1  X X+2 X+1 X+2  0  3 X+3  1  0
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3 X+1 X+2 X+2  3  0  X  1 X+1  1  X X+3 X+1  0  2 X+1  2 X+1 X+3 X+3  1 X+2 X+3 X+1  3  2 X+2 X+3  0  3  2

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+147x^36+482x^37+996x^38+1544x^39+1935x^40+2614x^41+2962x^42+3790x^43+3630x^44+3782x^45+3271x^46+2882x^47+1936x^48+1322x^49+752x^50+356x^51+185x^52+96x^53+51x^54+18x^55+6x^56+8x^57+2x^59

The gray image is a code over GF(2) with n=176, k=15 and d=72.
This code was found by Heurico 1.13 in 9.7 seconds.